There exist call and put options on one share of Options 'R' Real Inc. (ORR). Each option is EUROPEAN, expires exactly one year from today and has an exercise price of $45 per share. Assume no transaction costs and no taxes.

Suppose that the current riskless borrowing and lending interest rate from today until the option's expiration date remains 4.65%, and that

the current share price of ORR is $100.

Moreover, the likelihood that the stock price will fall to $45 (the exercise price) or lower is zero. ORR will not pay dividends over the life of the option.
 

a) What is the equilibrium price of the European put option? 

(Hint: How much would you pay for a put option that you will never?)

b) What is the equilibrium price of the European call option?

c) Suppose that TODAY you can exercise the option to get the stock. What are the intrinsic value and time value of the call option? Should you exercise the call TODAY? EXPLAIN. 

d) Suppose that the options above are American options.How will your answers to C above change? EXPLAIN.
 

e) Suppose that ORR will pay cash dividends of $5 to anyone who owns it today. Tomorrow morning, the stock prices will fall to $95. If you exercise the call option, you can either sell the stock for $100 or get the dividends and keep or sell the stock afterwards. ORR will not pay additional dividends over the life of the option.

Calculate the equilibrium price, intrinsic value, and time value of the European call option? (Assume that the equilibrium price of the European put remains the same.

f) Suppose that the call options above are American options. Will the equilibrium price of the American call be equal to, or higher than, that of the European call? EXPLAIN.